\newproblem{lay:1_1_26}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.1.26}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  Suppose the system below is compatible for all possible values of $f$ and $g$. What can you say about the coefficients $c$ and $d$?
	\begin{center}
		$\begin{array}{rcl} 2x_1+4x_2&=&f\\
		   cx_1+dx_2&=&g\\
		\end{array}$
	\end{center}
}{
   % Solution
	Let us construct the augmented matrix and apply row operations to reduce it
	\begin{center}
		\begin{tabular}{cc}
			  &
				$\left(\begin{array}{rr|r}
					 2 &  4 & f \\
					 c &  d & g \\
				\end{array}\right)$\\
			 $\mathbf{r}_2\leftarrow \mathbf{r}_2-\frac{c}{2}\mathbf{r}_1$ &
				$\left(\begin{array}{rr|r}
					 2 &  4 & f \\
					 0 &  d-2c & g-\frac{cf}{2} \\
				\end{array}\right)$\\
		\end{tabular}
	\end{center}
  If the system is compatible for any value of $f$ and $g$, then it must be that the coefficient $d-2c$ is different from 0 (if it were 0, then there would be combinations of
	$f$ and $g$ for which the system would be incompatible).
}
\useproblem{lay:1_1_26}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
